Click here to flash read.
arXiv:2405.02443v1 Announce Type: new
Abstract: In a recent work arXiv:2004.14450, it has been shown that $L$-functions associated with arbitrary non-zero cusp forms take large values at the central critical point. The goal of this note is to derive analogous results for twists of Dirichlet-type functions. More precisely, for an odd integer $q >1$, let $F$ be a non-zero $\mathbb{C}$-linear combination of primitive, complex, even Dirichlet characters of conductor $q$. We show that for any $\epsilon>0$ and sufficiently large $X$, there are $\gg X^{1-\epsilon}$ fundamental discriminants $8d$ with $X < d \leq 2X$ and ${(d, 2q)=1}$ such that ${|L(1/2, F \otimes \chi_{8d})| }$ is large.
Click here to read this post out
ID: 840123; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: May 7, 2024, 7:33 a.m.
Changes:
Dictionaries:
Words:
Spaces:
Views: 6
CC:
No creative common's license
No creative common's license
Comments: